In this paper we show that two ellipsoid algorithms can be used to train single-layer neural networks with general staircase nonlinearities. The ellipsoid algorithms have several advantages over other conventional training approaches including (1) explicit convergence results and automatic determination of linear separability, (2) an elimination of problems with picking initial values for the weights, (3) guarantees that the trained weights are in some “acceptable region,” (4) certain “robustness” characteristics, and (5) a training approach for neural networks with a wider variety of activation functions. We illustrate the training approach by training the MAJ function and then by showing how to train a controller for a reaction chamber temperature control problem.